Category: Relation and Functions

Question Number 132422 by john_santu last updated on 14/Feb/21 $$\mathrm{Given}\:\mathrm{P}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{polynomial}. \\ $$$$\:\mathrm{If}\:\mathrm{P}\left(\mathrm{x}+\mathrm{1}\right)\:+\:\frac{\mathrm{P}\left(\mathrm{x}\right)}{\mathrm{x}}\:=\:\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} −\mathrm{2} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{P}\left(\mathrm{x}\right)}{\mathrm{x}} \\ $$ Answered by bemath last updated on 14/Feb/21 Terms…

Question Number 66800 by mathmax by abdo last updated on 19/Aug/19 $${calculate}\:{U}_{{n}} =\int_{\frac{\mathrm{1}}{{n}}} ^{{n}} \:\:\:\frac{{arctan}\left({x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$$${and}\:{determine}\:{lim}_{{n}\rightarrow+\infty} {U}_{{n}} \\ $$$$\left.\mathrm{2}\right){find}\:{nature}\:{of}\:\Sigma\:{U}_{{n}} \\ $$ Commented by…

Question Number 66799 by mathmax by abdo last updated on 19/Aug/19 $${let}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\left(−\mathrm{1}\right)^{{k}} }{\:\sqrt{{k}}}\:\:{find}\:{a}\:{equivalent}\:{of}\:{S}_{{n}} \:{when}\:{n}\rightarrow+\infty \\ $$ Terms of Service Privacy Policy Contact:…

Question Number 66796 by mathmax by abdo last updated on 19/Aug/19 $${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} }{dx} \\ $$ Commented by mathmax by abdo last updated…

Question Number 66789 by mathmax by abdo last updated on 19/Aug/19 $${sove}\:{the}\:\left({de}\right)\:\:\:\left(\mathrm{1}+\mathrm{2}\sqrt{{x}}\right){y}^{'} −\left({x}+\sqrt{{x}−\mathrm{1}}\right){y}\:={xsin}\left(\mathrm{2}{x}\right) \\ $$ Commented by mathmax by abdo last updated on 20/Aug/19 $$\left({he}\right)\:\rightarrow\left(\mathrm{1}+\mathrm{2}\sqrt{{x}}\right){y}^{'}…